Question

describe the difficulty you would encounter if you assume that the solution of de is in the form of

Answer 1

\[y=\sum_{n=0}^{\infty} a _{n}(x-x _{0})^{n}=\sum_{n=0}^{\infty}a _{n}(x-0)^{n}=\sum_{n=0}^{\infty}a _{n}x ^{n}\]

Answer 2

consider \[x ^{2}y"+xy'+(x ^{2}-\frac{ 1 }{ 4 })y=0\]